The present invention relates to a computerized method for simulating deformation of a rubber compound with filler particles, more particularly to a method using a pseudo-two-dimensional rubber compound model capable of calculating a large deformation without increasing the model generation time.
In order to save time and cost for making prototypes of a rubber product made of a rubber compound, the use of a computer simulation for analyzing deformation of the rubber compound becomes popular in recent years.
Such simulation methods are disclosed in for example Japanese Patent Application Publication Nos. JP-A-2005-121535, JP-A-2005-146146, JP-A-2006-193560, JP-A-2008-122154, JP-A-2009-216612, JP-A-2009-276147, JP-A-2009-282569, JP-A-2010-205165, and JP-A-2010-49414.
Generally, the simulation methods are classified into a two-dimensional simulation method and a three-dimensional simulation method.
In a two-dimensional simulation method, based on a sectional image of a rubber compound obtained by the use of a microscope, a two-dimensional rubber compound model a1 (finite element model) is generated as shown in FIG. 8(a).
The two-dimensional rubber compound model a1 is made up of a model b1 of the rubber matrix and models c1 of filler particles dispersed in the rubber matrix, and each model is defined by two-dimensional elements e1.
on the rubber matrix model b1 and filler particle models c1, materials properties are defined.
Then, a deformation calculation (simulation) is performed under predetermined conditions.
The generation of such two-dimensional rubber compound model a1 is relatively easy when compared with the under-mentioned three-dimensional models.
However, the node points of each element e1 of the two-dimensional model are movable within only a two-dimensional plane, for example, movable only in x-direction and y-direction in a Cartesian coordinate system. There is no degree of freedom in z-direction perpendicular to the two-dimensional plane, namely, in the thickness direction of the rubber compound model a1.
On the other hand, in a three-dimensional simulation method, for example, based on a plurality of sectional images of a rubber compound obtained through a technique of computer tomography, a three-dimensional internal structure of the rubber compound is reconstructed.
Then, using the data of the three-dimensional internal structure, a three-dimensional rubber compound model a2 is generated for example, as shown in FIG. 8(b) wherein for convenience sake, the filler particles are illustrated by a sphere.
The three-dimensional rubber compound model a2 is made up of a model b2 of the rubber matrix and models c2 of the filler particles, and each model is defined by three-dimensional elements e2.
In comparison with a two-dimensional model, such three-dimensional rubber compound model a2 requires a longer time for the generation. In return, it is possible to simulate a relatively large deformation since the node points of each element e2 have three degrees of freedom in x-, y- and z-directions.
On the other hand, when a deformation simulation is performed using a two-dimensional rubber compound model a1 in which the density of the filler particles is locally or entirely high, if a large deformation occurs locally in the rubber compound model, there is a possibility that the deformation calculation is stopped. Particularly, since the deformation freedom is less in the two-dimensional rubber compound model a1, with the progress of deformation, the strain of the elements e1 is increased, and often it becomes impossible to continue the deformation calculation.
As explained, in comparison with the three-dimension simulation method, the two-dimensional simulation method has the merit of shorter model generation time, but it is weak in large deformation calculation.
If the 2D and 3D rubber compound models a1 and a2 are the same in the volume percentage of the filler particles, then the 3D model can simulate a larger deformation than the 2D model.